A Mathematician's Way of Learning Golf

This is another true story that will show you what an interesting variety of people I meet and how many and different ways there are of thinking about golf.

One day a player walked into my shop and inquired for me. I happened to be out, but he booked a lesson for the following day. He was an internationally famous mathematician and scientist and by no means of the abstract unpractical type.

"Do you know anything about mathematics?" he asked as we walked over to the practice ground.

If I had not known who he was, I might have dropped into the trap but, "Not a figure!" says I.

"But they told me you had been a schoolmaster/' he said, "and that you had a leaning towards the scien­tific, especially in golf"

"That is true. But I was a pretty poor schoolmaster, and what even the good ones know about mathematics is no use in golf. You can't work out the golf swing in graphs, you know."

"Oh, who told you you could not?"

"No one told me, but what I know about graphs does not seem to bear any more relationship to golf than does let us say the green grass on the fairway here to the Eiffel Tower, which you can see away in the dis­tance yonder."

"Green grass!"He laughed ironically. "Who told you it is green? And is it?"

"Oh I don't know! Anyway I thought you had come out here to have a golf lesson, not to plumb the depths of my ignorance."

"Do you know anything about Einstein?" he asked completely undisturbed.

"If by Einstein you mean his theory," said I getting one back on him, "of course I know nothing about it. At least, all I do know is that only twelve people in the world are said to understand it and you're one of them."

"Actually you probably know quite a lot about it," he said, "only you cannot express it in simple language."

"Well no more can you," said I briefly. For if you could, many more people would understand it."

"Let us see! Firstly you must realize that golf is a four-dimensional game . . . time of course being the fourth."

"That is a good one," said I. "What are the other three?"

"Well, I am coming to that. Will you please play me a shot or two?"

We had a caddie out to scout the balls, and there was another watching from out to the right of us. I took a few preliminary swings and then hit a very sweet shot off the turf with my brassie, clean and long with just a little pull at the end.

"Now," he said, "what did you see?"

"Well," said I, "I did not lift my head too soon, so I did not see the ball rise. I saw it in the air and then saw it carry a bit to the left as it dropped."

"Good. Now what did the caddie see? He saw the ball come out of the sky too, but he saw it drop to the right. And the fellow out in the wood there saw a simple rise and fall without deviation. So you see that you three fellows would all have described the same operation quite differently; all the descriptions might have been accurate yet they would (on the surface) have described different flights. That is relativity."

"But what has that to do with golf?"

"Nothing perhaps, except to warn you against hasty conclusions even when you see things with your own eyes. So do not be too sure the grass is green!"

"Oh drat you and your green grass! What do I care if it is green or blue or black. . . ."

"I knew a painter who said it was black," he said.

"Drat him too," said I. "You are getting me hot and bothered. What about this lesson you came out to have?"

"I am having it," he said. "In my own way. I am getting my mind right for the real work, when it comes."

"By which time," said I, "111 probably be a raving lunatic. And don't ask me how I know I am not one now. I do know the answer to that one!"

"Oh! Do you?" he said quizzically. "But tell me this: how many dimensions do you swing your club head through?"

After a pause, to scratch my head I suggested, "Two, I should think. Up and down."

"Not so bad! You are only a third out. You said 'Up? and 'down? but your club also goes 'around/ "

"Well, around is not a dimension."

"Oh, isn't it! Don't you tell your pupils to swing wide?"

"Yes I do. I tell them to take the club head back wide and throw it out in the widest arc they can that is what I call width."

"Well, that is better than nothing. But do your pupils all understand it that way? I did not."

"I can't help what you do not understand."

"But you should. You are paid by me to make me understand."

"Yes, I know. But have you heard the character sketch one Englishman a damned fool, two English­men a club, three Englishmen a great Empire? Well, I am just one Englishman!"

"Yes, I guessed that early on. But I am trying to understand the swing my way. The trouble with you Pros is that you only understand the swing your way; so you want us to understand it your way too. That is why you are really very little use to anyone except people of low intellectual grade. They do not under stand anything anyhow so it does not matter what you tell them. Those who become good learn by imitation, those who do not work things out in their own minds which is fatal because they have nothing to think with"

"I don't entirely agree with that. They are difficult to teach, but so are you!"

"Exactly! But in my case that is your own fault. You do not know enough about golf to make me understand it my way. They told me you were a scientific teacher . . . rubbish! You tell me to 'swing through an inclined plane' that is where people get the idea you are scientific. You are just an advanced slogan-monger. Telling the best girl of some wealthy gent to swing through an inclined plane! What does she know of inclined planes?"

"You're asking me!" said I.

"You do not swing through an inclined plane," he said. "You swing through a vertical plane but with depth."

"Well, perhaps you are right. But how the hell can I tell a man to swing deep? When he thinks of depths, he thinks of Australia and bunkers and his grave. You can't have depth sideways."

"Yes, I see that. I know which is right; so 2 + 1 = 4 impresses me because of its contradiction to the truth."

"So the negative impresses you the more. Now! You tell me that to make the ball roll is the greatest art of the golfer."

"Yes I do."

"You also say that to make the ball roll you must put 'top-spin' on it."

"Agreed."

"Well that, I must point out, is a negative also be­cause no one can put top-spin on a golf ball."

"Oh no! You want me to believe that when I putt a ball all along the ground, and it runs and runs and runs, rolling over and over and over, I have not put top-spin on it?

"You have not put the fraction of a particle of top-spin on it."

"But I can make the ball roll and you can't. Why is that then?"

"Because with your skill and experience you can make your club head 90° vertical and can pass it over the ground to connect with the ball square to its horizontal axis. Then as the bottom of the ball is stuck to the ground by the friction set up by gravity and the op is free to move, the top moves first and you set up your over and over movement. Just as if your feet sud­denly stuck in the ground as you were running, you would fall flat on your face."

"But you are not going to tell me that I can't impart what I call top-spin in different degrees and so make one ball run more than another. Watch this . . . and this . . . and this . . . ," I said, playing various shots.

"Yes, very skillfully done. But all you have done is to put less back-spin on some shots than on others. That is what I meant when I said 'top-spin' in golf is a negative. The only spin you can put on a golf ball is back-spin. To put on top-spin is a physical impossibilityas you will see if you think out where and at what angle the ball would have to be struck to impart it."

"Well, what does it matter to me what sort of spin you call it, so long as I can produce the effect I want?"

"As a player, it does not matter to you at all. The skill with which you can control spin makes you an out­standing player, no matter what you call it. But as a teacher, it does matter to you because the fact that you call things by their wrong names prevents me learning from you. Your teaching capacity is negative."

"Thank you," said I. "Fortunately there are plenty of people who do not agree with you. And anyway if that is so, why are you taking this lesson?"

"I love talking to simple people."

"Hell! Do you know that I have beaten Henry Cotton and anyone who can do that is not so simple!"

"It is because you play golf in the simple way that you beat him! Experience has taught you the easiest way of playing. By dint of that experience and unceas­ing practice, you have learned to draw a straight line in the most simple way."

"A straight line?"

"What is a straight drive but a straight line? a long one and drawn without a ruler too! Also it is in four dimensions. Yet you are simple enough to wonder why people cannot play golf and why you cannot teach them."

"Put like that it does sound complex. But now I come to think of it, I play golf in one dimension only-straight ahead."

"And what about time?"

"I ignore it. I play in one dimension only straight ahead."

"Like a worm crawling straight to its hole?"

"Yes, exactly, except in my figure!"

"You mean to tell me that you only try to knock the ball along the ground?"

"Yes."

"When you play high shots over trees? When you deliberately put on back-spin, do you conceive all that as golf in one dimension?"

"I do."

"Well, why didn't you tell me that before? Here we have been troubling ourselves with Einstein, only to find now that you play in one dimension only."

"Well, it's a reasonable simplification, isn't it?"

"Possibly so; it is if you mean what I think you do . . . that you play golf in four dimensions with a one-dimensional outlook."

"I don't know about my dimensional outlook; what I try to feel is that I am in a position to play straight along the ground."

"Well, that certainly seems a very simple outlook and in your case it is undeniably effective. Do you think that I will ever be able to play along the ground?"